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Abstract

In this chapter the authors describe systems and control theory concepts for systems biology and the corresponding implications for medicine. The context for a systems approach to the life sciences is outlined, followed by a brief history of systems and control theory. The technical aspects of systems and control theory are then described in a way oriented toward their biological and medical application. This description is then used as a reference base against which to indicate specific areas where systems and control theory aspects of systems biology have strong medical implications. Specifically, two systems biology projects are described as examples of where methods from systems and control theory play an important role.

Introduction

In this chapter the authors give their experiences gained working at the interface between the biological/medical sciences and the physical/engineering systems sciences. In doing so we attempt to convey the contributions that the physical, mathematical and engineering sciences have made, and will continue to make, to innovations in biology and medicine. In this context we stress the role played by systems and control theory in the development of general principles for biological systems, and in particular the understanding of dynamical phenomena in biology and medicine. According to our experiences, systems methods are influencing the biology research sector through a series of evolutionary scientific steps, as follows:

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Stage 1: High-throughput biochemical instrumentation was (and continues to be) developed to provide rapid measurement and generation of data.

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Stage 2: To meet the need to process data generated in stage 1, data processing methods are being developed to extract information from very large data records.

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Stage 3: The information from stage 2 is used to calibrate mathematical models with which to visualise an underlying biological process. This is the current evolutionary state in systems biology.

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Stage 4: Control and systems theory are applied to the mathematical models of stage 3 to provide understanding of biological behaviour and underlying principles.

In summary, the sequence goes from:

measurement → data → information → visualisation → understanding.

The current state of the art is that the value of in-silico simulation of biological phenomena is becoming appreciated. Even so, most biological measurement techniques are designed to collect static data, whereas time course data is required to develop mathematical models for visualising system dynamics by in-silico simulation. It is not always appreciated that, as a result of poor data, the calibration and structural correctness of mathematical models is often suspect. Likewise, there is currently little appreciation of the fundamental importance of control and systems theory in understanding biological and physiological phenomena and principles.

On the other hand, the role of systems and control theory is clearly established in the medical community through the understanding that it gives to physiological function. Under the historical influence of Claude Bernard’s ideas, as embodied in Cannon’s concept of homeostasis (Bayliss, 1966, Cannon, 1932), feedback control is central to many aspects of current medical understanding, although this is usually intuitive and non-theoretical in nature (Tortora, 2003). Since Cannon’s work in the 1930’s, other researchers have expanded upon the homeostatic feedback principle (Sterling, 2004) in its specific medical and physiological contexts. In the meantime however, systems and control theory has expanded scientifically and progressed to become a mature scientific discipline with fundamental relevance to all areas of scientific endeavour. Throughout this 70-year period of separate development, the medical concepts of control systems and the mathematical tools of control and systems theory have diverged. The aim of this chapter is to reconnect the medical ideas of feedback with mainstream theory by explaining areas where control and systems theory can contribute. We consider this to be vitally important to our scientific futures. For, as indicated above and documented in the recent report Systems Biology: a vision for engineering and medicine (Royal Academy, 2007), the use of systems theory and control concepts will be essential to our understanding of biological systems for medicine.

Key Terms in this Chapter

Closed Loop Feedback Control: This is the process of continuously measuring the output of a system and using a modified version of the measured output at the systems input so as to alter the overall performance of the system.

Matlab: The name of a widely used proprietory software package that is especially suited to the simulation of dynamical system models and their analysis. It is produced by MathWorks Inc. It is adapted from a public domain package of the same name – public domain equivalents are available as Octave and Scilab.

Transfer Function: The name given to the frequency domain representation of a functional system module with distinct input and output points.

Dynamical System: An assembly of components or sequence of reactions whose performance can only be completely described by a study of its behaviour over time.

State Space: The name given to the mathematical space into which mathematical models are put for systems and control studies using temporal analysis of the time course data. State space (or time domain) analysis is suitable for linear or non-linear systems analysis. This is therefore highly suited to medical and systems biological analysis.

Systems Theory: The set of mathematical techniques used to analyse and understand the (dynamical) behaviour of systems.

Feedback: The technique of monitoring information from one part of a system and using it to modify a system element at some point prior to the monitoring point. If the monitored information is used to add to the system element it is positive feedback , if it is used to subtract from the system element it is negative feedback.

Data Analysis: The analysis of time course data from a system in order to understand the nature of the signal generating mechanisms associated with a system. These are often unwanted noise or errors in the process and are used to modify or correct the mathematical model.

Mathematical Model: A set of equations, usually ordinary differential equations, the solution of which gives the time course behaviour of a dynamical system. The set of equations for example 1 is an example of a mathematical model.

Linearity: Is the property of a system where if two inputs sequences X a and X b produce responses Y a and Y b , then X a +X b will produce the response Y a +Y b . The system is said to be linear – most biological and medical systems do not satisfy this criteria and are said to be non-linear.

Pharmacodynamics: This refers to the analysis of the biochemical and physiological effects of drugs and the mechanisms in which they work.

Control Theory: The set of mathematical techniques used to analyse and design control systems.

Stability Analysis: That part of systems and control theory which is used to study and predict the stability or instability characteristics of a system from a knowledge of the mathematical model.

System Identification: The analysis of time course data from a system in order to deduce the nature of the system and the values of parameters that could be used in a mathematical model to reproduce the time course data in simulation.

Pharmacokinetics: This refers to the dynamical mechanism by which a drug is absorbed, and processed by the body

In-silico Simulation: The use of a special computer programme to solve the equations of a mathematical model and produce a set of plots of model parameters over time.